Finite element analysis for 3-dimensional large scale problem by using domain decomposition methods

使用域分解方法对 3 维大规模问题进行有限元分析

• 批准号: 15360044
• 负责人: KANAYAMA Hiroshi
• 金额: $ 9.73万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15360044/
• 关键词: domain decomposition method; large scale problem; eddy current problem; thermal convection problem; Stokes equation; iterative solver; balancing preconditioner; parallel computation; 共役勾配法; BDD法; 前処理付反復法; 近似逆行列前処理; 合同な部分領域への領域分割; 有限要素法コードのベクト

A.Numerical computations of large scale magnetic problems by finite element method:First, we have developed computational codes for time-harmonic eddy current problems and nonlinear magnetostatic problems. To make the codes efficient, then we have considered the reduction of their computational costs, and the enhancement of applicable problems, for example, a permanent magnet or a moving obstacle.B.Numerical solver for linear systems with symmetric coefficient matrices:We have considered the convergence of MRTR method based on the minimization of residuals. Moreover, we have developed several precondisioners, which come from robust incomplete Cholesky factorization, and have shown their efficiency by appling to some real problems.C.Application of a substracturing method to discretized Stokes equations:We have established a coarse space of a balancing precondisioner for applying to discretized Stokes equations.D.Error estimates of finite element methods for thermal convection problems:We have established error estimates of a class of finite element methods for thermal convection problems with variable coefficients.E.Realization of highly efficient BDD methods for large scale structural analysis:We have developed incomplete BDD methods, improved its parallel efficiency, and realized nonstationary structural analysis with about 10 million DOF problems.

A.大规模磁问题的有限元数值计算：首先，我们开发了时谐涡流问题和非线性静磁问题的计算代码。为了使代码高效，我们考虑了降低其计算成本，并增强适用问题，例如永磁体或移动障碍物。B.具有对称系数矩阵的线性系统的数值求解器：我们考虑了基于残差最小化的MRTR方法的收敛性。此外，我们还开发了几种来自鲁棒不完全Cholesky分解的预处理器，并通过应用于一些实际问题显示了它们的效率。C.减法方法在离散Stokes方程中的应用：我们建立了平衡预处理器的粗空间适用于离散斯托克斯方程。D.热对流问题有限元方法的误差估计：我们已经建立了一类热对流问题有限元方法的误差估计E.实现大规模结构分析的高效BDD方法：我们开发了不完全BDD方法，提高了其并行效率，实现了约1000万自由度问题的非平稳结构分析。

项目成果

Seismic response analysis of nuclear pressure vessel model with ADVENTURE System on the Earth Simulator

地球模拟器上利用 ADVENTURE System 进行核压力容器模型地震响应分析

• 发表时间: 2005
• 期刊: Journal of The Earth Simulator 2
• 作者: Ogino;M.;Shioya;R.;Kawai;H.;Yoshimura;S.
• 通讯作者: S.

Effectiveness of A-φ method in a parallel computing with an iterative domain decomposition method

A-φ方法在迭代域分解方法并行计算中的有效性

• 发表时间: 2005
• 期刊: Proceedings of COMPUAG2005 I
• 作者: Kanayama;H.;Sugimoto;S.
• 通讯作者: S.

An enhancement of efficiency for robust incomplete factorization preconditioning based on A-orthogonalization process.

基于A正交化过程的鲁棒不完全因式分解预处理效率的提高。

• 发表时间: 2004
• 期刊: IPSJ transactions on advanced computing systems Vol.45
• 作者: Ikeda;Y.;Fujino;S.;Kakihara;M.;Inoue;A.
• 通讯作者: A.

Verification of large-scale analysis of 3-d nonlinear magnetostatic problems

3 维非线性静磁问题大规模分析的验证

• 发表时间: 2005
• 期刊: Proceedings of COMPUMAG2005, TEAM WORK SHOP
• 作者: Kanayama;H.;Sugimoto;S.
• 通讯作者: S.

Advanced general-purpose finite element solid analysis system ADVENTURE_SOLID on the Earth Simulator

地球模拟器上的先进通用有限元固体分析系统 ADVENTURE_SOLID

• 发表时间: 2004
• 期刊: ASME/JSPE Pressire Vessels and Piping Conference 482
• 作者: Shiya;R.;Ogino;M.;Kawai;H.;Yoshimura;S.
• 通讯作者: S.